What is the branch of Mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations?

The branch of mathematics you are referring to is called Algebra. Algebra involves the use of letters, symbols, and numbers to represent and solve equations and formulas. In algebra, variables (usually represented by letters like $x$, $y$, or $z$) are used to denote unknown values, and these can be manipulated according to the rules of algebraic operations. This allows for the formulation and solving of a wide range of mathematical problems, from simple equations to complex functions. Algebra serves as a foundation for many advanced fields of mathematics and is essential for understanding concepts in calculus, geometry, and beyond.